Antenna selection with RF imbalance

ABSTRACT

A method for selecting antennas in a multiple-input, multiple-output wireless communications network that includes multiple stations is presented. Each station includes a set of transmit RF chains and a set of receive RF chains, and each RF chain is connectable to a set of antennas. A first station transmits a training frame for each possible subset of the set of antennas, and the set of transmit RF chains are connected to the subset of antennas according to a connection mapping rule while transmitting each training frame. A subchannel matrix is estimated in a second station for each frame. The subchannel matrices are combined to obtain a complete channel matrix. A particular subset of the antennas is selected according to the complete channel matrix. The set of transmit RF chains is connected to the selected particular subset of antennas to transmit data from the first station to the second station.

FIELD OF THE INVENTION

This invention relates generally to multiple-input, multiple-output(MIMO), wireless communication systems, and more particularly toselecting antennas in MIMO systems.

BACKGROUND OF THE INVENTION

Multiple-input, multiple-output (MIMO) techniques can significantlyincrease system capacity in a scattering environment of a wirelessnetwork. However, multiple antennas increases hardware complexity andcost because, in a typical system, each transmit/receive antennarequires a separate radio frequency (RF) chain including amodulator/demodulator, an AD/DA converter, an up/down converter, and apower amplifier. In addition, the processing complexity at the basebandalso increases with the number of antennas.

Antenna selection (AS) can reduce the number of RF chains while stilltaking advantage of the capacity/diversity increase provided by multipleantennas. The idea is to select a submatrix from a complete channelmatrix according to some predetermined criterion. To perform antennaselection, the complete channel matrix is estimated by sending trainingframes to measure the complete channel state information (CSI). Thetraining frames can be sent in the same physical layer packet or bymultiple packets.

Conventionally, on transmitting or receiving these AS training frames,the device conducting antenna selection switches different antennasubsets to the RF chains and estimates the corresponding subchannelsmatrices. The selection is based on the complete channel matrix composedof the estimated subchannels matrices.

However, conventional antenna selection schemes ignore the fact thateach possible connection of a RF chain to an antenna introduces oneunique RF response containing the effects of both amplitude gain andphase shift. As a result, in some circumstances, distortions areinevitable for antenna selection, because the selected antennas used fordata transmission and reception may be connected to RF chains differentfrom those used during training.

In the data transmission phase, the actual channel associated with theselected antennas may not be identical to that used in the trainingphase. This phenomenon is known as a RF imbalance problem.

It is desired to correct the RF imbalance problem in MIMO systems.

SUMMARY OF THE INVENTION

The embodiments of the invention provide solutions for antenna selectionthat reduce an RF imbalance problem. A first solution trains with allpossible antenna subsets, instead of the disjointed subsets as inconventional schemes. To avoid large overhead, a second solution definescalibration procedures to correct the distortion.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a MIMO system according to an embodiment ofthe invention;

FIG. 2 is a block diagram of an antenna selection cycle according to anembodiment of the invention;

FIG. 3 is a block diagram of training and calibration initiated by atransmit station; and

FIG. 4 is a block diagram of training and calibration initiated by areceive station.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

System Overview

FIG. 1 shows a MIMO communication system according to an embodiment ofthe invention. The system includes a first station (STA A) 110, a secondstation (STA B) 120, and wireless channels 130. Either station canoperate in receive or transmit mode. Generally, the station thattransmits data is called the transmit station or transmitter, and thestation that receives the data is called the receive station orreceiver. The data are transmitted and received using a baseband signal.

Hereinafter, a ‘set’ is defined as including one or more elements; thenumber of elements in a ‘subset’ is equal to or less than the number ofelements in the corresponding set.

Each station includes a set of receive (Rx) RF chains 111 and a set oftransmit (Tx) RF chains 112, both connected to a set of antennas 113 byswitches 114. Generally, in MIMO devices, the number of antennas islarger than the number of RF chains. Therefore, a subset of antennas isselected 115 from the set of total available antennas by a methodaccording to an embodiment of the invention during an antenna selection(AS) training phase as described herein. The selection method can beinitiated by either the transmitter or the receiver, and the selectioncan be conducted at the transmitter and/or at the receiver.

Association Phase

During an initial association phase, not shown, the stations exchangeinformation about the number of RF chains, the number of antennas, andthe type of antenna selection. In particular, the type of informationcontained in a feedback packet, e.g., whether information is indices ofthe antennas to be used, and/or a full (instantaneous) channel stateinformation (CSI), and/or an average channel state information istransmitted during that time or, alternatively, as part of the feedbackpacket.

Training and Data Transmission Phases

As shown generally in FIG. 2, each AS training cycle is composed of anantenna selection training phase 201 and a data transmission phase 202.The cycle can be repeated periodically, or as the channel environmentchanges. Several AS training frames 211 are transmitted in each AStraining phase 201. Each of the frames is transmitted from and/orreceived by one subset of antennas to be selected. The antenna selection210 is based on a complete channel matrix. The complete channel matrixis estimated from a combination of the subchannel matrices estimatedfrom the AS training frames 211. The selected antennas are connected tothe RF chains by the switches 114 before the data frames 212 aretransmitted during the data transmission phase 202. Another antennaselection cycle can be initiated when the current selected antennasubset is outdated, or when a predetermined time interval has elapsed.

System Model for MIMO Systems with Antenna Selection

In a MIMO system with conventional antenna selections, a transmitstation A has a set of N_(A) antennas with N_(A) _(—) _(SS) transmit RFchains, and a receive station B has a set of N_(B) antennas with N_(B)_(—) _(SS) receive RF chains. In the data transmission phase 202, arelationship between a transmitted signal and a received signal in aflat-fading channel can be expressed asr _(B) =F _(B) ^(H)({tilde over (H)} _(A→B) F _(A) s _(A) +n)where r_(B) is a N_(B) _(—) _(SS)×1 received signal vector, s_(A) is aN_(A) _(—) _(SS)×1 transmitted signal vector, and {tilde over (H)}_(A→B)is a N_(B)×N_(A) equivalent channel matrix containing physical channelresponses and an effect of transmit and receive RF responses.

A noise vector n has N_(B)×1 entries that are independent andidentically distributed (i.i.d.) zero-mean circular complex Gaussianrandom variables with variance N₀. F_(A) is a N_(A)×N_(A) _(—) _(SS)transmit antenna selection matrix, and F_(B) is a N_(B)×N_(B) _(—SS)receive antenna selection matrix. Both F_(A) and F_(B) are submatricesof an identity matrix. The equivalent channel matrix after antennaselection is a N_(B) _(—) _(SS)×N_(A) _(—) _(SS) matrix H_(eq)=F_(B)^(H){tilde over (H)}_(A→B)F_(A), which is a submatrix of the channelmatrix {tilde over (H)}_(A→B). The superscript ‘H’ means the conjugatetranspose, which is used here for selection by the receiver.

The determination of F_(A) and F_(B) optimizes the capacity of thechannel and the signal-to-noise ratio (SNR). If only one side antennaselection is considered, one of F_(A) and F_(B) equals the identitymatrix, and the corresponding number of RF chains equals the number ofantennas.

Antenna selection is performed by switching each output signal of atransmit RF chain to a selected transmit antenna, or each input signalof a selected receive antenna to a receive RF chain. The required numberof RF chains to modulate/demodulate the transmitted/received signals isless than the total number of available transmit/receive antennas.Therefore, the cost of the system is reduced.

Conventional antenna selection schemes ignore the fact that theequivalent channel {tilde over (H)}_(A→B) in the data transmission phasecontains the impact caused by RF responses. Specifically,{tilde over (H)} _(A→B) =C _(B,Rx)(F _(B))H _(A→B) C _(A,Tx)(F _(A)),where H_(A→B) is the actual propagation channel between the transmitantennas of STA A and the receive antennas of STA B. C_(A,Tx) (F_(A)) isa N_(A)×N_(A) diagonal matrix whose i^(th) diagonal element,[C_(A,Tx)(F_(A))]_(ii), collects the RF response corresponding to thei^(th) transmit antenna, which is a function of the antenna selectionmatrix F_(A).

If the i^(th) row in F_(A) contains all zeros, then the i^(th) antennais not selected, and [C_(A,Tx)(F_(A))]_(ii)=0. If an element at thei^(th) row and l^(th) column of F_(A) is one, then the i^(th) antenna isselected and is connected to the l^(th) transmit RF chain during thedata transmission phase. [C_(A,Tx)(F_(A))]_(ii)=α_(li) ^((Tx)) is acomplex number characterizing both the amplitude and phase shift of theRF response corresponding to the connection of transmit RF chain l andantenna i.

Therefore, in C_(A,Tx)(F_(A)) there are N_(A) _(—) _(SS) non-zerodiagonal elements. C_(B,Rx)(F_(B)) is similarly defined as[C_(B,Rx)(F_(B))]_(jj)=β_(li) ^((Rx)) if the element at the j^(th) rowand l^(th) column of F_(B) is one.

In the m^(th) conventional antenna selection training phase, arelationship between a transmitted signal and a received signal can beexpressed as:r _(B,t)(m)=T _(B) ^(H)(m)({tilde over (H)} _(A→B) T _(A)(m)s _(A,t)+n),where S_(A,t) is a N_(A) _(—) _(SS)×1 training vector known at bothstations; r_(B,t) is the N_(B) _(—) _(SS)×1 received training vector atSTA B; and T_(A)(m) and T_(B)(m) are the switching matrices in them^(th) AS training frame, whose values are predetermined, indicating theconnections of the RF chains to the m^(th) antenna subset. All theseantenna subsets are exclusive with each other. For example, ifN _(A)=4×N _(A) _(—) _(SS)=2,N _(B)=2,N _(A) _(—) _(SS)=2and ${{T_{A}(1)} = {{\begin{bmatrix}1 & 0 \\0 & 1 \\0 & 0 \\0 & 0\end{bmatrix}\quad{and}\quad{T_{A}(2)}} = \begin{bmatrix}0 & 0 \\0 & 0 \\1 & 0 \\0 & 1\end{bmatrix}}},$then there are totally M = ⌈N_(A)/N_(A_SS)⌉⌈N_(B)/N_(B_SS)⌉training frames.

Then, STA B can estimate the complete channel matrix, which is used forAS computations, by combining the M subchannel matrices. Consequently,by ignoring channel estimation errors from training frame m, theestimated subchannel matrix is{tilde over (H)}′ _(A→B)(m)=T _(B) ^(H)(m)C _(B,Rx)(T _(B)(m))H _(A→B) C_(A,Tx)(T _(A)(m))T _(A)(m),and the AS is based on the following estimated complete channel matrix:{tilde over (H)}′ _(A→B) =C′ _(B,Rx) H _(A→B) C′ _(A,Tx),where the diagonal matrix C′_(A,Tx) contains all non-zero diagonalelements, and [C′_(A,Tx)]_(ii)=[C_(A,Tx)(T_(A)(m))]_(ii) if the i^(th)antenna is trained by the m^(th) training frame. Each antenna is trainedonly once, and C′_(B,Rx) is similarly defined.

RF Imbalance

The antenna selection distortion caused by the RF imbalance can bedescribed as follows. Antenna selection is based on the estimatedcomplete matrix {tilde over (H)}′_(A→B), i.e., using a certain AScriteria X, the selection can be expressed as:$\left\{ {F_{A,{opt}},F_{B,{opt}}} \right\} = {\underset{F_{A},F_{B}}{{\arg\quad\max}\quad}{{X\left( {F_{B}^{H}{\overset{\sim}{H}}_{A\rightarrow B}^{\prime}F_{A}} \right)}.}}$There are $N = {\begin{pmatrix}N_{A} \\N_{A\_ SS}\end{pmatrix}\begin{pmatrix}N_{B} \\N_{B\_ SS}\end{pmatrix}}$possible antenna subsets to be selected according to the aboveexpression. However, if F_(A,opt), F_(B,opt) are selected in the datatransmission phase, the equivalent channel becomesH _(eq) =F _(B,opt) ^(H) C _(B,Rx)(F _(B,opt))H _(A→B) C _(A,Tx)(F_(A,opt))F _(A,opt),and X(H_(eq)) may not be optimal due to the differences between the RFresponses in training phase and in data transmission phase. Therefore,the selection {F_(A,opt), F_(B,opt)} may, in fact, be suboptimal.

In the above example of N_(A)=4, N_(A) _(—) _(SS)=2, N_(B)=2, N_(A)_(—SS) =2, i.e., only STA A conducts AS, F_(B)=T_(B)=I so C_(B,Rx) isalways fixed. Then, the selection is based on${\overset{\sim}{H}}_{A\rightarrow B}^{\prime} = {C_{B}^{({Rx})}{{H_{A\rightarrow B}\begin{bmatrix}\alpha_{11}^{({Tx})} & \quad & \quad & \quad \\\quad & \alpha_{22}^{({Tx})} & \quad & \quad \\\quad & \quad & \alpha_{13}^{({Tx})} & \quad \\\quad & \quad & \quad & \alpha_{24}^{({Tx})}\end{bmatrix}}.}}$

If antennas 1 and 3 are selected at STA A during data transmissionphase, then${\overset{\sim}{H}}_{A\rightarrow B}^{\prime} = {C_{B}^{({Rx})}{{H_{A\rightarrow B}\begin{bmatrix}\alpha_{11}^{({Tx})} & \quad & \quad & \quad \\\quad & 0 & \quad & \quad \\\quad & \quad & \alpha_{23}^{({Tx})} & \quad \\\quad & \quad & \quad & 0\end{bmatrix}}.}}$Obviously, there is a distortion caused by α₁₃ ^((Tx))≠α₂₃ ^((Tx)), andtransmit antennas 1 and 3 may not be the optimal selection.

RF Chain to Antenna Connection Mapping Rule

To improve the conventional selection process, we use the followingconnection mapping rule. The RF chains have corresponding RF chainindices and the antennas have corresponding antenna indices. For anyselected antenna subset, the connection of RF chains to antennas is asfollows. Without loss of generality, a RF chain with smaller RF chainindex always connects to an antenna with smaller antenna index. Forexample, in the above example, if antennas 1 and 3 are selected at STAA, then transmit RF chain 1 is connected to antenna 1, and transmit RFchain 2 is connected to antenna 3.

According to the connection mapping rule, in the AS training phase 201and the data transmission phase 202, there are a total of N_(A) _(—)_(SS)×(N_(A)−N_(A) _(—) _(SS)+1) connections of RF chains and antennasubsets at STA A, and all the possible RF responses can be expressed as:$\begin{matrix}{\begin{matrix}\alpha_{11}^{({Tx})} & \alpha_{22}^{({Tx})} & \cdots & \alpha_{N_{A\_ SS}N_{A\_ SS}}^{({Tx})} \\\alpha_{12}^{({Tx})} & \alpha_{23}^{({Tx})} & \cdots & \alpha_{N_{A\_ SS}{({N_{A\_ SS} + 1})}}^{({Tx})} \\\vdots & \vdots & ⋰ & \vdots \\\alpha_{1{({N_{A} - N_{a\_ SS} + 1})}}^{({Tx})} & \alpha_{2{({N_{A} - N_{A\_ SS} + 2})}}^{({Tx})} & \cdots & \alpha_{N_{A\_ SS}N_{A}}^{({Tx})}\end{matrix}.} & (1)\end{matrix}$

For example, in the above N_(A)=4, N_(A) _(—) _(SS)=2 case, all possibleRF responses include:

α₁₁ ^((Tx)) α₂₂ ^((Tx))

α₁₂ ^((Tx)) α₂₃ ^((Tx))

α₁₃ ^((Tx)) α₁₂ a₂₃

α₁₃ ^((Tx)) α₂₄ ^((Tx)).

There are totally 2×3=6 possible values of α_(li) ^((Tx)). Note that theabove connection mapping rule does not introduce any performance losscompared with conventional antenna selection schemes, which do not takeRF responses into considerations.

Antenna Selection Considering RF Imbalance

One solution for the RF imbalance problem is to train all chains incombination with all possible subsets of antennas, instead of onlydisjoint subsets of antennas, as in the prior art. Consequently, in eachAS training phase 201, there are N training frames, one for eachpossible subset of antennas connected to the transmit RF chainsaccording to the above connection mapping rule. If the m^(th) possiblesubset is selected, i.e., F_(A, opt)=T_(A)(m), F_(B, opt)=T(m), then, inboth the training frame m and the data transmission phase, the estimatedsubchannel matrix is $\begin{matrix}{{{\overset{\sim}{H}}_{A\rightarrow B}^{\prime}(m)} = {{T_{B}^{H}(m)}{C_{B,{Rx}}\left( {T_{B}(m)} \right)}H_{A\rightarrow B}{C_{A,{Tx}}\left( {T_{A}(m)} \right)}{T_{A}(m)}}} \\{= {F_{B,{opt}}^{H}{\overset{\sim}{H}}_{A\rightarrow B}{F_{A,{opt}}.}}}\end{matrix}$

Thus, there is no distortion between the AS training phase 201 and thedata transmission phase 202. The drawback of this scheme is theincreased training overhead because N>M.

Calibration for Antenna Selection

In addition, calibration can be performed to reduce the RF imbalanceproblem. The RF responses cannot always be determined because the RFresponses vary with the environment over time, e.g., changes infrequency, temperature, etc. Therefore, an over-the-air calibrationprocesses can be used. The overhead for calibration is small because thecalibration processes can be conducted infrequently, e.g., only when theenvironment varies.

Calibration for Transmit Antenna Selection

FIG. 3 shows the calibration procedure when the transmitter (STA A)conducts antenna selection. STA 110 sends a training frame 301 with thefollowing transmit RF chain and antenna connections:RF1→Ant1,RF2−Ant2, . . . ,RFN _(A) _(—) _(SS) →AntN _(A) _(—) _(SS),i.e., the transmit RF responses equal to the first row of expression(1). On receiving this training frame, STA B 120 estimates 310 thecorresponding subchannel matrix {tilde over (H)}′_(A→B)(1).

STA A sends the other (N_(A)−N_(A) _(—) _(SS)) training frames 302, ineach of which the connections of RF chains to antennas follows thecorresponding row in expression (1). On receiving these training frames,STA B 120 estimates 310 the corresponding subchannel matrices {tildeover (H)}′_(A→B)(2)˜{tilde over (H)}′_(A→B)(N_(A)−N_(A) _(—) _(SS)+1).

After receiving all the (N_(A)−N_(A) _(—) _(SS)+1) training frames301-302, STA B feeds back 320 all the estimated subchannel matrices toSTA A. STA A determines 330 RF imbalance TX correction coefficientsbased on all the estimated subchannel matrices fed back from STA B.

If N_(B)>N_(B) _(—) _(SS) and STA B also conducts receive antennaselection, on receiving all the (N_(A)−N_(A) _(—) _(SS)+1) trainingframes, STA B uses a predetermined subset of receive antennas, eachconnected to a predetermined receive RF chain.

The correction coefficients are determined as follows, by ignoringchannel estimation errors,${{{\overset{\sim}{H}}_{A\rightarrow B}^{\prime}(1)} = \begin{bmatrix}{\overset{\sim}{h}}_{{A\rightarrow B},11}^{(11)} & {\overset{\sim}{h}}_{{A\rightarrow B},12}^{(22)} & \cdots & {\overset{\sim}{h}}_{{A\rightarrow B},{1N_{A\_ SS}}}^{({N_{A\_ SS}N_{A\_ SS}})} \\{\overset{\sim}{h}}_{{A\rightarrow B},21}^{(11)} & {\overset{\sim}{h}}_{{A\rightarrow B},22}^{(22)} & \cdots & {\overset{\sim}{h}}_{{A\rightarrow B},{2N_{A\_ SS}}}^{({N_{A\_ SS}N_{A\_ SS}})} \\\vdots & \vdots & ⋰ & \vdots \\{\overset{\sim}{h}}_{{A\rightarrow B},{N_{B\_ SS}1}}^{(11)} & {\overset{\sim}{h}}_{{A\rightarrow B},{N_{B\_ SS}2}}^{(22)} & \cdots & {\overset{\sim}{h}}_{{A\rightarrow B},{N_{B\_ SS}N_{A\_ SS}}}^{({N_{A\_ SS}N_{A\_ SS}})}\end{bmatrix}},$where {tilde over (h)}_(A→B,n) _(B) _(i) ^((li))=β_(l) _(B) _(n) _(B)^((Rx))h_(A→B,n) _(B) _(i)α_(li) ^((Tx)) stands for the equivalentchannel involving all the RF responses, and h_(A→B,n) _(B) _(i) is theactual physical channel coefficient from transmit antenna i to receiveantenna n_(B) connected to receive RF chain l_(B). Therefore, β_(l) _(B)_(n) _(B) ^((Rx)) is the corresponding receive RF response at STA B, andsimilarly α_(li) ^((Tx)) is the transmit RF response at STA A with theconnection of transmit antenna i and transmit RF chain l. {tilde over(H)}′_(A→B)(2)˜{tilde over (H)}′_(A→B)(N_(A)−N_(A) _(—) _(SS)+1) can beexpressed similarly based on different transmit RF chain and antennaconnections following the corresponding rows of the expression (1).

As in expression (1), in any case antenna 2 at STA A can only beconnected to RF chain 1 or 2. Then, for a predetermined n_(B), thefollowing calculation can be conducted:${\kappa_{l\quad 2} = {\frac{{\overset{\sim}{h}}_{{A\rightarrow B},{n_{B}2}}^{(12)}}{{\overset{\sim}{h}}_{{A\rightarrow B},{n_{B}2}}^{({l\quad 2})}} = {\frac{\beta_{l_{B}n_{B}}^{({Rx})}h_{{A\rightarrow B},{n_{B}2}}\alpha_{12}^{({Tx})}}{\beta_{l_{B}n_{B}}^{({Rx})}h_{{A\rightarrow B},{n_{B}2}}\alpha_{l\quad 2}^{({Tx})}} = \frac{\alpha_{12}^{({Tx})}}{\alpha_{l\quad 2}^{({Tx})}}}}},$for l=1 and 2, and k₁₂=1. Then, k₁₂ is used as the correctingcoefficient, which is multiplied on the baseband stream transmitted fromthe l^(th) RF chain whenever the l^(th) RF chain is connected to antenna2. Therefore, any transmission from antenna 2 leads to a transmit RFresponse of α₁₂ ^((TX)) at STA A in the AS training phase 201 and in thedata transmission phase 202.

Similarly, for the i^(th) transmit antenna:${\kappa_{li} = {\frac{{\overset{\sim}{h}}_{{A->B},{n_{B}i}}^{({\min{\{ L_{i}\}}i})}}{{\overset{\sim}{h}}_{{A->B},{n_{B}i}}^{({li})}} = \frac{\alpha_{\min{\{ L_{i}\}}i}^{({Tx})}}{\alpha_{li}^{({Tx})}}}},{{{for}\quad l} \in L_{i}}$where L_(i) is the set of RF chain indices that are possible to beconnected to antenna i as defined in expression (1). Then, k_(li) isapplied whenever RF chain l is connected to antenna i, and anytransmission from antenna i leads to a corresponding transmit RFresponse of α_(min) ^((Tx)) _({L) _(i) _(}i). As special cases, transmitantennas 1 and N_(A) are always connected to RF chain 1 and N_(A) _(—)_(SS), respectively, so no correction is needed for antennas 1 andN_(A). By doing the same calculations up to I=N_(A)−1 and by applyingthe results, at any time the equivalent complete channel matrix can beexpressed as: ${{\overset{\sim}{H}}_{A\rightarrow B} = \begin{matrix}{C_{B,{Rx}}{H_{A\rightarrow B} \cdot}} \\{{diag}\left\{ {\alpha_{11}^{({Tx})},\alpha_{12}^{({Tx})},\ldots\quad,\alpha_{\min{\{ L_{i}\}}i}^{({Tx})},\ldots\quad,\alpha_{N_{A\_ SS}N_{A}}^{({Tx})}} \right\}}\end{matrix}},$and there is no distortion between the AS training phase and the datatransmission phase for STA. Note that these correction coefficients areapplied in both the AS training phase and the data transmission phase,and is equivalent to replacing the ones in F_(A) or T_(A)(m) by thecorresponding correction coefficients.

The above calculation can be repeated N_(B) _(—) _(SS) times, withn_(B)=1 . . . N_(B) _(—SS) . The resultant N_(B) _(—SS) sets ofcorrection coefficients can then be averaged over a time period toreduce the impact from channel estimation errors.

Calibration for Receive Antenna Selection

FIG. 4 shows the calibration procedure when the receiver (STA B) 120conducts antenna selection. All the possible receiver RF responsescorresponding to the connections of receive RF chain and receiveantennas are: $\begin{matrix}\begin{matrix}\beta_{11}^{({Rx})} & \beta_{22}^{({Rx})} & \ldots & \beta_{N_{B\_ SS}N_{B\_ SS}}^{({Rx})} \\\beta_{12}^{({Rx})} & \beta_{23}^{({Rx})} & \ldots & \beta_{N_{B\_ SS}{({N_{B\_ SS} + 1})}}^{({Rx})} \\\vdots & \vdots & ⋰ & \vdots \\\beta_{1{({N_{B} - N_{B\_ SS} + 1})}}^{({Rx})} & \beta_{2{({N_{B} - N_{B\_ SS} + 2})}}^{({Rx})} & \ldots & {\beta_{N_{B\_ SS}N_{B}}^{({Rx})}.}\end{matrix} & (2)\end{matrix}$

STA B 120 sends a calibration training request (CTRQ) 401 to STA A 110,which contains the number of training frames 410 (N_(B)−N_(B) _(—)_(SS)+1) the receiving station requires.

STA A responds by transmitting the (N_(B)−N_(B) _(—) _(SS)+1) trainingframes 410 from a predetermined set of transmit antennas. STA B receiveseach training frame by using the receive RF chain and receive antennaconnections defined in the corresponding row of expression (2), andestimates 420 the corresponding subchannel matrix.

After receiving all the (N_(B)−N_(B) _(—) _(SS)+1) training frames 410,STA B 120 determines 430 the RF imbalance receive (Rx) correctioncoefficients based on all the estimated subchannel matrices. Thisdetermination is similar as for the transmit antenna selection case: forreceive antenna j and for lεL_(j),${\lambda_{lj} = {\frac{{\overset{\sim}{h}}_{{A->B},{jn}_{A}}^{\prime{({\min{\{ L_{j}\}}j})}}}{{\overset{\sim}{h}}_{{A->B},{jn}_{A}}^{\prime{({lj})}}} = {\frac{\beta_{\min{\{ L_{j}\}}j}^{({Rx})}h_{{A->B},{jn}_{A}}\alpha_{l_{A}n_{A}}^{({Tx})}}{\beta_{lj}^{({Rx})}h_{{A->B},{jn}_{A}}\alpha_{l_{A}n_{A}}^{({Tx})}} = \frac{\beta_{\min{\{ L_{j}\}}j}^{({Rx})}}{\beta_{lj}^{({Rx})}}}}},$where {tilde over (h)}′_(A→B,jn) _(A) ^((lj)) is the estimated channelcoefficient from any transmit antenna n_(A) connected to transmit RFchain l_(A) to receive antenna j corresponding to the connection ofreceive RF chain l to receive antenna j at STA B, and L_(j) is the setof RF chain indices that are to be connected to antenna j as defined inexpression (2). The correcting coefficient λ_(ij) is multiplied on thebaseband stream received by the l^(th) receiving RF chain, whenever itis connected to antenna j at STA B, and consequently any reception byantenna j, in the AS training phase or in the data transmission phase,leads to a corresponding receive RF response of β_(min{Lj}j) ^((Rx)).The equivalent complete channel matrix can be expressed as:${\overset{\sim}{H}}_{A\rightarrow B} = \begin{matrix}{{diag}{\left\{ {\beta_{11}^{({Rx})},\beta_{12}^{({Rx})},\ldots\quad,\beta_{\min{\{ L_{j}\}}j}^{({Rx})},\ldots\quad,\beta_{N_{B\_ SS}N_{B}}^{({Rx})}} \right\} \cdot}} \\{H_{A\rightarrow B}{C_{A,{Tx}}.}}\end{matrix}$

Hence, there is no distortion between the AS training phase and the datatransmission phase at STA B. These correction coefficients are appliedin both the AS training phase and the data transmission phase, and isequivalent to replacing the ones in F_(B) or T_(B) (m) by thecorresponding correction coefficients.

The above calculations can be repeated N_(A) _(—) _(SS) times, withn_(A)=1 . . . N_(A) _(—) _(SS). The resultant N_(A) _(—) _(SS) sets ofcorrection coefficients can be averaged over a time period to reduce theimpact from channel estimation errors.

When both stations perform antenna selections, their calibrations can beconducted one after the other. After the first station, either atransmit or receive station, completes calibration, the first stationuses a predetermined subset of antennas each connecting to apredetermined RF chain to assist the calibration of the second station.As a result, after the defined calibration procedure(s), the equivalentcomplete channel matrix is:${\overset{\sim}{H}}_{A\rightarrow B} = \begin{matrix}{{diag}{\left\{ {\beta_{11}^{({Rx})},\ldots\quad,\beta_{\min{\{ L_{j}\}}j}^{({Rx})},\ldots\quad,\beta_{N_{B\_ SS}N_{B}}^{({Rx})}} \right\} \cdot}} \\{{H_{A\rightarrow B} \cdot {diag}}\left\{ {\alpha_{11}^{({Tx})},\ldots\quad,\alpha_{\min{\{ L_{i}\}}i}^{({Tx})},\alpha_{N_{A\_ SS}N_{A}}^{({Tx})}} \right\}}\end{matrix}$which always contains fixed transmit and receive RF responses. Then,antenna selection training can be done in the conventional way withoutdistortions. Only M training frames are required in each AS trainingphase, in which the training signals are transmitted from and/orreceived by antenna subsets exclusive with each other.

The above transmit or receive AS calibration procedure can also beconducted in a normal transmit/receive AS training phase, in whichmultiple consecutive AS training frames are transmitted from, orreceived by disjointed antenna subsets without considering RF imbalance.One example is the AS training scheme described in PCT PatentApplication number PCT/US2005/042358, “Method for Selecting Antennas andBeams in MIMO Wireless LANs,” filed in the U.S. Receiving Office by Guet al. on Nov. 21, 2005 and incorporated herein by reference. To do so,the number of the consecutive training frames is modified to be equal tothat required for calibration calculation. For example, if N_(B)=N_(B)_(—) _(SS), with the RF chain/antenna connection constraints of Equation(1) for transmit AS calibration, this number is N_(A)−N_(A) _(—) SS,instead of $\left\lceil \frac{N_{A}}{N_{A\_ SS}} \right\rceil.$

In the case of transmit AS calibration, STA A in FIG. 3 sendsN_(A)−N_(A) _(—) _(SS)+1 calibration training frames from the antennasubsets with the RF chain connections according to expression (1). STA Btreats these frames as normal AS training frames, i.e., STA B estimatessubchannel matrices from them and feeds the complete channel matricesback. Finally STA A calculates the transmit correction coefficients.

In the case of receive AS calibration, STA B in FIG. 4 informs STA A ofthe required number of calibration training frames by a normal AStraining request. STA A then responds by sending the correspondingnumber of AS training frames with no knowledge of whether these trainingframes are used for normal receive AS training or for receive AScalibration. STA B receives these frames by the antenna subsets with theRF chain connections according to expression (2), and estimates thesubchannel matrices. Finally, STA B determines the receive correctioncoefficients.

In such a way, the calibration procedure does not introduce a newsignaling protocol.

Variations

The above processes can be applied to the cases where the system isfrequency-selective, such as orthogonal frequency division multiplexing(OFDM) networks. In OFDM networks, the above training or calibrationprocedures are conducted for each subcarrier, or in each group ofsubcarriers.

In the case that each selected antenna subset is connected to the RFchains with predetermined ordering, the AS training process has moretraining frames in each AS training phase to estimate the subchannelmatrix corresponding to each possible RF chain and antenna connection.The calibration procedure also sends sufficient training frames tocompensate for each possible connection, e.g., if any RF chain canconnect to any antenna, in the calibration of the transmitter at STA A,L_(i)={1, 2, . . . , N_(A) _(—) _(SS)}, ∀i, and thereforeα_(2i)^((Tx))…  α_(N_(A_SS)i)^((Tx))all need to be corrected so that the connection of any RF chain withantenna i always leads to a transmit RF response α_(li) ^((Tx)).

In the calibration procedures, the compensation for the RF chainsconnected to a particular antenna can also be applied with respect to acoefficient other than α_(min{L) _(i) _(}) ^((Rx)) or β_(min{L) _(j)_(}j) ^((Rx)). Any calibration procedure by which any transmit orreceiver antenna brings a fixed RF response to the equivalent channelcan be used.

The calibration procedure is based on the fact that different RF chainsand antenna connections, i.e., switch positions, lead to differentamplitude and phase responses. On the other hand, if the switch does notintroduce any distortions depending on its positions, i.e., for anyparticular RF chain its connections to different antennas result insubstantially identical RF responses, i.e., all antennas have similarmatching properties with the RF chain, then the calibration procedurecan be simplified.

Specifically, this is so because the RF imbalance is caused only bydifferent responses of the RF chains. If the connection orderingconstraint described above is applied or not, then it is sufficient tocalibrate every RF chain only once: in the first training frame connectthe first RF chain to antenna i, then connect the second RF chain toantenna i for transmitting or receiving the second training frame, . . ., connect the last RF chain to the same antenna in the last trainingframe.

Finally, α_(1i)^((Tx))…  α_(N_(A_SS)i)^((Tx))are compensated with respect to one fixed value at the transmitter afterfeeding back all the measured subchannel matrices, each with a singletransmit antenna, or, β_(1i)^((Rx))  ⋯  β_(N_(B_SS^(i)))^((Rx))are directly compensated with respect to one fixed value at thereceiver, based on all the measured subchannel matrices, each with asingle receive antenna. In this scenario, the RF imbalance problem iscaused only by the difference among RF chains, the compensated RFchains, with antenna i, also lead to no distortion when connected to allthe other antennas.

Although the invention has been described by way of examples ofpreferred embodiments, it is to be understood that various otheradaptations and modifications can be made within the spirit and scope ofthe invention. Therefore, it is the object of the appended claims tocover all such variations and modifications as come within the truespirit and scope of the invention.

1. A method for selecting antennas in a multiple-input, multiple-outputwireless communications network including a plurality of stations, eachstation including a set of transmit RF chains and a set of receive RFchains, wherein each RF chain is connectable to a set of antennas,comprising the steps of: transmitting, from a first station to a secondstation, a training frame for each possible subset of the set ofantennas, and wherein the set of transmit RF chains are connected to thesubset of antennas according to a connection mapping rule whiletransmitting each training frame; estimating, in the second station, asubchannel matrix for each frame; combining the subchannel matrices toobtain a complete channel matrix; selecting a particular subset of theantennas according to the complete channel matrix; and connecting theset of transmit RF chains to the selected particular subset of antennas,to transmit data from the first station to the second station.
 2. Themethod of claim 1, further comprising: feeding back the subchannelmatrices from the second station to the first station; determining, inthe first station, transmit RF imbalance correction coefficients basedon the estimated subchannel matrices; combining the subchannel matricesin the first station; and selecting a particular subset of the antennasaccording to the complete channel matrix and the transmit RF imbalancecorrection coefficients.
 3. The method of claim 2, further comprising:multiplying a baseband signal with the RF imbalance correctioncoefficients corresponding to the set of transmit RF chains and theselected particular subset of antennas, in which the baseband signalcarries the transmit data.
 4. The method of claim 1, further comprising:determining, in the second station, receive RF imbalance correctioncoefficients based on the estimated subchannel matrices; and combiningthe subchannel matrices in the second station.
 5. The method of claim 1,further comprising: selecting, in the second station, a particularsubset of antennas, connected to the set of receive RF chains accordingto the complete channel matrix, to receive the transmit data.
 6. Themethod of claim 1, further comprising: multiplying a baseband signalwith the RF imbalance correction coefficients corresponding to theconnection of RF chains and antennas over which the baseband signal isreceived.
 7. The method of claim 1, further comprising: determining atransmit RF imbalance correction coefficient for a connection between anl^(th) RF chain and an i^(th) antenna using channel state information,such that the connection has a fixed baseband RF response.
 8. The methodof claim 1, further comprising: determining a receive RF imbalancecorrection coefficient for a connection between an l^(th) RF chain andan j^(th) antenna using channel state information, such that theconnection has a fixed base band RF response.
 9. The method of claim 1,further comprising: transmitting, from the second station to the firststation, a calibration training request.
 10. The method of claim 2,further comprising: averaging the transmit correction coefficients overa time period.
 11. The method of claim 4, further comprising: averagingthe receive correction coefficients over a time period.
 12. The methodof claim 1, in which the network is an orthogonal frequency divisionmultiplexing (OFDM) network.
 13. The method of claim 12, furthercomprising: performing a calibration procedure for each subcarrier ofthe OFDM network.
 14. The method of claim 1, in which the RF chains haveRF chain indices and the antennas have antenna indices, and a RF chainwith smaller RF chain index always connects to an antenna with smallerantenna index.
 15. The method of claim 1, further comprising:determining RF imbalance correction coefficients based on the estimatedsubchannel matrices.